FOURIER APPROXIMATION

This applet explores how well a periodic function's Fourier series approximates the original function.

In the applet \(f(t)\) is the original function and \(f_A(t)\) is its Fourier approximation give by summing the first \(n\) terms of its Fourier series. Both functions are given a color and the entire applet is color coded.

Choice of function
There is a drop down menu (just above the n-slider) which lets you choose the function \(f(t)\).

Sliders and checkboxes
The number of terms \(n\) in the Fourier approximation (\(f_A(t)\)) is set by the n-slider.
The two checkboxes just above the n-slider control whether or not to show the graphs of \(f(t)\) and \(f_A(t)\).

Graphs
The left-hand graphing window shows the graphs of \(f(t)\) and \(f_A(t)\). The small rectangle in this window shows the part of the graph that is zoomed in on in the right-hand window.

Time and function values
The current time \(t\) is set by using the mouse to move the small dot on the t-axis in the left-hand graphing window. When it is in range, this dot also appears in the right-hand graphing window. Small dots are also placed on the graphs of \(f\) and \(f_A\). These dots can also be grabbed and moved with the mouse.
The current time and associated function values are given just below the left-hand graph.

Graph value readouts
For both graphs: if your mouse is in the graphing window the coordinates of the mouse position are displayed above the graph.